In this paper, we study quantum error-correcting codes from cyclic codes over the ring R, where R is a non-chain extension of Fp. We give a method to obtain self-orthogonal codes over Fp as Gray images of linear and cyclic codes over the ring R. Finally, we derive the parameters of associated quantum error-correcting codes.
In the paper, we consider a finite non-chain commutative ring [Formula: see text], where [Formula: see text]. We mainly study the construction of quantum codes from cyclic codes over [Formula: see text]. For this, we obtained self-orthogonal codes over [Formula: see text] as gray images of linear and cyclic codes over [Formula: see text], then these codes over [Formula: see text] correspond to a cyclic code over [Formula: see text] of odd length [Formula: see text] used to determine the parameters of the quantum codes.
On Quantum Codes Obtained From Cyclic Codes Over F2+uF2+u2F2
Let R=F2+uF2+u2F2 be a non-chain finite commutative ring, where u3=u. In this paper, we mainly study the construction of quantum codes from cyclic codes over R. We obtained self-orthogonal codes over F2 as gray images of linear and cyclic codes over R. The parameters of quantum codes which are obtained from cyclic code over R are discussed.